An Array Experiment with Magnetic Variometers Near the Coasts of South-east Australia
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Geophys. J . R. astr. SOC.(1972) 29, 49-64.
An Array Experiment with Magnetic Variometers Near the
Coasts of South-east Australia
F. E. M. Lilley and D. J. Bennett
(Received 1972 January 27)
Summary
An array of magnetic variometers has been operated in the south-east
corner of the Australian mainland, observingthe coast effect simultaneously
in two dimensions for the first time. The observations are presented as sets
of variograms in the time domain and as contour maps of certain para-
meters in the frequency domain. Vertical field response functions are
determined for each station, and the concept of fitting a surface over the
area, using the response functions to define tangential planes, is introduced.
By choosing different polarizations of the horizontal fields, the effects
of the two coast lines, which are approximately at right angles to one
another, can be distinguished. A major result is that for the East Coast,
the enhanced vertical variations are not accompanied by significantly
enhanced horizontal variations. The distinctive coast effect of the Bass
Strait is noted, especially concerning the amplitude of the variations in the
horizontal fields. There is a suggestion of an anomalous region in western
Victoria, which may correlate with the ‘ Newer Volcanics ’ rock structure
of the area. A quantitative interpretation is planned for a subsequent
paper.
Introduction
This paper describes observations from an experiment held during the first half of
1971, in which an array of instruments recording transient geomagnetic variations
was kept in operation across south-east Australia, from the Great Australian Bight
to the Tasman Sea. It is the first such array experiment to be reported from Australia,
though it was actually the second to be carried out there. An earlier one was conducted
across south central Australia in 1970, (Gough, McElhinny & Lilley, in preparation).
The area covered by the experiment is shown in Fig. 1. There are several reasons
for conducting a geomagnetic depth sounding experiment in south-east Australia.
Firstly, a number of high heat flows have been measured in the area, both in the
Highlands Fold Belt of the Tasman geosyncline to the east, and in the ‘Newer
Volcanics ’ of Victoria to the west, (Jaeger 1970). Volcanic activity in the latter area
has been dated to as recently as 6000yr BP (Gill 1967). It is possible that remnants
of the magma chambers will still be at elevated temperatures, and the principle of
mapping higher temperatures in the crust and upper mantle through their consequence
of higher electrical conductivity has been one of the longstanding interests of geo-
magnetic deep sounding.
Secondly, of the seven array studies which had been made since Gough & Reitzel
(1967) first developed an instrument which could be economically reproduced in
49
450 F. E. M. Lilley d D.J. Bennett
1 I I -' 1
-
Fro. l(a) Map of the observing sites; (b) Major tectonic features in the array area.
The rectangle drawn around the observing sites is the frame for all subsequent
array diagrams.Array experiment witb magnetic variometers 51
large sets, up to the time in question all had been remote from coasts. It was therefore
of interest to carry out an array study near a coast, to see if the extra information from
recording the variation fields over a two-dimensional area, rather than along a one-
dimensional line, could help in clarifying the cause of the enhancement of vertical
variations near coast lines. This is the phenomenon known as the coast-effect; it was
first described by Parkinson (1959).
An array study for this purpose might be especially rewarding because good
control may be hoped for over the variation fields of all three geomagneticcomponents,
and as pointed out by Bullard & Parker (1971), the horizontal components of the
coast effect may be particularly diagnostic as to its cause.
The experiment
Twenty-five variometers of the Gough-Reitzel type were installed at airstrips, at
sites shown in Fig. 1. The twenty-sixth station of Fig. 1 is the permanent observatory
Toolangi, (TLG), for which the records are published with the permission of the
Director of the Australian Bureau of Mineral Resources. The portable instruments
were installed and retrieved by a road party, and serviced in the interim by light
aircraft: an ideal mode of transport for the purpose. The instruments were completely
buried and operated unattended between servicing visits (every three weeks). A high
degree of successful recording time was returned, and the instruments were calibrated
at the start and again at the finish of every service visit.
During the observing period, 1971 February 3 to May 15, a variety of magnetic
activity occurred. The data of this paper are based upon two particular periods of
activity, which were chosen as optimum events for analysis. The times of the events
were March 19, 1100-1800, and April 1 1, 0800-1800. The instruments recorded the
three variation components H (magnetic north), D (magnetic east), and Z (vertically
down), but because the magnetic declination ranges over some four degrees across
the array, it was decided to work with the alternative horizontal components of X
(geographic north) and Y (geographic east). The corresponding sets of X, Y and 2
variograms are presented in Figs 2 and 3.
Data reduction
The original records being on photographic film, a certain amount of manipulation
was necessary to reduce them to digital form. This part of the data analysis follows
that given in the first such array study, by Reitzel et al. (1970). The steps taken weie
the printing of ( x 10) enlargements of the sections of the data film of interest; and
then semi-automatic digitization of these enlargements. The data were adjusted for
the calibration constants of the individual instruments, and corrected for a minor
interaction between two of the sensing elements, in each case. Series for X and Y
were computed from those for H and D. The frequency spectra were obtained by
direct Fourier transformation; the data series of interest was multiplied by a sin’
taper over its first and last 10 points, and a linear trend removed. Sections of the
variograms which could be considered as complete individual transients were chosen
for analysis, so that the whole of the frequency spectrum obtained by transforming
them could be taken to be valid. This is in contrast to the analysis of a time series
which has clearly suffered serious truncation, and in this sense the study of geomagnetic
events such as bays is fortunate, in that the whole disturbance may frequently be
analysed complete.
Zeros could be added to increase the length of a time series, without altering the
frequency spectrum of the event. Fourier transformation of such a longer time series
results in finer definition of the frequency spectrum, and representative spectra areX Z
NWR
GBN
CMD
NRD
HAY
ERD
MDR
MRY
CMA
C RG
CRW
ECH
WPF
NHL
B BL
BM B
MFD
T LG
ART
MC T
OR 9
TGN
TY B
DNM
HTN
GBR
iloo
1100 ll0C il00 1800
FIG.2. Variograms for the event of 1971 March 19m
v)
0081 0080 Ooel 0080
..
YE3
NlH
WNa
BAl
N31
Em
13W
1W
311
adw
EWE
188
1HN
JdM
H33
MY3
3Y3
VR3
A.uW
W W
ow
AVU
OYN
v
avo
NE3
X54 F. E. M.Ulky .nd D. J. Bennett
1; - _ cycles/ min)
75 50 15 75 50 15 15 50
period (min)
1L liL
10
0
10
75
10
10
30 40
25
10
75
10
50
30 40
25
I0
75
20
50
30 40
-3
freq ( x i 0
cycles/ min)
period ( m i d
loh-*Li;L
10
2k-
I
10
75
10
50
30 40
I5
10
75
20
10
30 40
15
10
75
YO
50
30 40 freq ( x lo3
cycles/min)
period (min)
0 -3
I0 10 30 40 I0 10 30 40 10 10 30 40 freq ( x i 0
75 15 ?I5 0 I5
. . . . . cycles/min)
50 75 50 period (min:
Fro. 4. Spectra of four stations for the event of 1971 April 11, 1500-1800hr.
Spectral amplitudes are in units of 90 gamma /cycle /min.Array experiment with magnetic variorneters 55
presented in Fig. 4. Particular frequencies and polarizations were chosen, and for these
the Fourier transform parameters of amplitude and phase were plotted on base maps,
and contoured. Representative examples of these are presented in the next section.
Polarization parameters for the horizontal variations were calculated following the
monochromatic theory of Born & Wolf (1959). A summary of the relevant formulae
follows, (adapted for the fact that the X - Y axes of geomagnetism are reversed from
the usual configuration taken for 2-dimensional x - y axes).
If a disturbance has horizontal components of
X = a2 cos ( o t + 6 )
Y = a, C O S W t
then the point (X, Y) traces out an ellipse with the passage of time.
Define a, (0 < a Q 4 2 ) such that
a2
tan a = -
r\ X AMP
A Z AMP
. . .
no. 5. Fourier transform parameter maps for 1971 March 19, 1215-1515 hr, at
period 81.9 min, with ellipse of horizontal polarization. Units of phase are
minutes; units of amplitude are 21 gamma /cycle /min.56 F. E. M.Lilley and D. J. Bennett
The principle semi-axes a and b of the ellipse and the angle $, (0 4 Ic/ < n) which the
major axis makes anticlockwise with geographic east are specified by the formulae
0 < $ < +n if cosS > 0
az+b2 = a l z + a z 2
in < $ < n if cos6 < 0
tan 2 Ic/ = (tan 2 4 cos 6
Ic/ = 0 if cosd = 0 and a , > a,
sin 2%= (sin 2 4 sin 6
$ = +n if cosS = 0 and a , c a,
where x, (- n/4 c x < n/4) is an auxiliary angle which specifies the shape and
orientation of the ellipse:
tanX= + -ba .
If sin6 > 0, the ellipse is described in a clockwise sense, and if sin6 < 0, anti-
clockwise. For sin6 = 0, or if either a , or a, is zero, the ellipse degenerates to a line
of linear polarization.
The values a,, a2 and 6, as functions of the angular frequency o,come from
I
#. 2 PHASE
~~
FIG.6 . Fourier transform parameter maps for 1971 March 19, 1500-1800 hr, at
period 85.3min, with ellipse of horizontal polarization. Units of phase are
minutes; units of amplitude are 21 gamma /cycle/min.Array experiment with magnetic variometers 57
X AMP
O b L . :.
I I
h Y AMP
(ii) (V)
FIG. 7. (ixiii) Fourier transform parameter maps for 1971 March 19, 1500-
1800hr, at period 33-6min. Units of amplitude are 21 gamma/cycle/min.
(ivxvi) Fourier transform parameter maps for 1971 April 11, 1500-1800 hr, at
period 186.2 min. Units of amplitude are 30 gamma/cycle/min. The ellipses
shown are those of horizontal polarization.
Fourier transforms of selected events in the time domain. The particular definition
of the Fourier transform adopted in this paper is
00
g(o) = ff(t) exp (- iwt) dt .
-00
Results from spectral analysis
The parameters from the spectral analyses may be presented for any particular
frequency in the form of contour maps. While it would be desirable, if possible, to
use a frequency for which the spectra of the vertical components at all stations are at
maxima, for a 3-dimensional conductivity structure there may be no reason to expect
such general peaks to occur. The polarization characteristics of the horizontal
variation fields are of crucial importance, and consequently the periods chosen have
been decided upon largely for the sake of obtaining certain polarizations in the
horizontal plane. This means many values have been taken which occur on the sides58 F. E. M. Lilley and D. J. Bennett
of lobes in the computed frequency spectra, and the importance of a whole spectrum
being valid is again emphasized.
Figs 5, 6 and 7 show a selection of the maps thus produced. The appropriate
ellipse of polarization of the horizontal fields drawn on each one is for the central
northern part of the area, that part most remote from the coasts. In most cases, data
from BRD, HAY, NRD and ECH have been combined to give a representative
ellipse. Thus Fig. 5, chosen for a period of maximum powei in 2,shows the response
of the area to a field polarized mainly southeast-northwest. Fig. 6 shows the response
for a polarization mainly southwest-northeast, and Fig. 7 shows the response, for
two different periods, to nearly linear north-south polarization. The significance of
the maps will be further discussed below.
Station response functions and a ‘ response surface ’
In geomagnetic variation studies, it is common to seek a fit of observed data to the
equation
2 =AX+BY (1)
where all quantities are functions of frequency. 2, X and Y have in-phase and
quadrature components, and the response (or transfer) functions, A and B, are
complex constants. Denoting the real and imaginary parts of a quantity by the
subscripts r and i, equation (1) may be expanded as
Z, = A,X,+B, X-AiXi-Bi Yi (2)
Zi = A , X i + B , Yi+AiX,+Bi X (3)
These equations may be compared to the relationship first proposed by Parkinson
(1 959), who developed a graphical method equivalent to fitting
AZ = A , A X + B , A Y (4)
where A X , A Y and A 2 are actual in-phase changes of field over some successive time
intervals, and A , and B, are real constants. Equation (4) defines a plane, and if data
which satisfy this equation are plotted in a u, u, w Cartesian co-ordinate system,
(where the geometric u, u, w axes are parallel to the magnetic X, Y, 2 axes), the
horizontal component of the downwards normal to the plane which results is known
as Parkinson’s vector.
Equation (2) does not correspond exactly to equation (4), but estimates of A, and
B, are commonly taken to represent A , and B,, and thus to define the Parkinson plane.
A second plane, it is to be noted, is similarly defined by the imaginary components,
A i and Bi.
If observations are made at a number of closely-spaced stations, the determination
of two particular planes at each one suggests the mapping of two surfaces over the
area, to be defined by the simple condition that the planes at each station shall be
parallel to the tangential planes of the surfaces there. The problem would be to
determine surfaces
wr = fr(u, 0 ) and wi = f i (u,0 )
given
at every point where there is an observing station. Because A and B are functions of
frequency, there will in fact be families of surfaces, corresponding to variation of the
frequency value.
By power spectral analysis of the two periods of magnetic activity shown in Figs
2 and 3, estimates of A and B for each station were computed by a method essentiallyArray experimmt with magnetic variometem 59
Table 1
Station Code Geographic co-ords Ar Ai Br Bi
Ararat ART 37" 19's 143"WE 0.55 0.14 -0.12 0.09
Bombala BBL 36" 55' 149" 11' 0.41 0.23 -0.05 -0.14
Benambra BMB 36" 58' 147" 42' 0.37 0 -0.13 -0.06
Balranald BRD 34" 36' 143" 34' 0.24 0.06 0 -0.02
Cooma CMA 36" 18' 148" 58' 0.30 0.07 -0.23 -0.05
Cootamundra CMD 34O 37' 148" 02' 0.21 0.06 -0.17 -0.04
Corryong CRG 36" 11' 147" 53' 0.29 0.05 -0.15 -0.02
Corowa CRW 35" 59' 146" 22' 0.24 0.11 -0.06 -0.03
Derrinallum DNM 37" 54' 143" 11' . 0.69 0.10 -0.13 -0.11
Echuca ECH 36" 08' 144" 46' 0.25 0.10 0.04 -0.05
Goulburn GBN 34" 49' 149" 44' 0.29 0.03 -0.32 -0.04
Mt Gambier GBR 37" 44' 140" 46' 0.80 0.09 0-15 -0.03
Hay HAY 34" 31' 144" 50' 0.19 0.02 -0.03 -0.06
Hamilton HTN 37" 39' 142" 03' 0.70 0.09 0.01 0.01
Mallacoota MCT 37" 36' 149" 43' 0.80 -0.12 -0.58 0.12
Mildura MDR 34" 14' 142" 04' 0.20 0.11 0.04 -0.05
Mansfield MFD 37" 02' 146" 08' 0.36 0.05 -0.08 -0.15
Moruya MRY 35" 54' 150" 08' 0.46 0.03 -0.58 0.02
Nhill NHL 36" 20' 141" 38' 0.33 0.11 0.16 -0.09
Narrandera NRD 34" 42' 146" 31' 0.20 0.08 -0.07 -0.04
Nowra NWR 34" 57' 150" 32' 0-54 0.04 -0.40 0.10
Orbost ORB 37" 47' 148" 36' 0.71 -0.12 -0.22 -0.03
Traralgon TGN 38" 12' 146" 28' 0.27 0.16 -0.04 -0.05
Toolangi TLG 37" 33' 145" 28' 0.22 0.18 0.05 -0.01
Tyabb TYB 38" 16' 145" 10' 0.26 0.14 0.12 -0.04
Wycheproof WPF 36" 04' 143" 14' 0.35 0.08 -0.03 0.02
following that given by Everett & Hyndman (1967). These estimates are listed in
Table 1 for the period of 80min, which corresponds to Fig. 5. On the assumption
that the real and imaginary parts of both A and B all have the same normal error
distribution, a common standard deviation for all values has been estimated to be of
order 0-3. (For Nowra and Bombala, for which only one period of magnetic activity
was analysed, it is 0.5). Parkinson vectors computed from the real parts of the A and
B values are plotted in Fig. 8. They are consistent with vectors for other sites in the
area published previously by Parkinson (1959), Everctt & Hyndman (1967), and
Bennett & Lilley (1971).
The two surfaces which can be defined, everywhere tangential to the planes of the
in-phase and quadrature response functions respectively, are by no means unique.
As an experiment to determine one such surface for the in-phase response fucctions
of Table 1, however, a polynomial was taken of degree just sufficiently high to exactly
fit the observational data. Subsequent experience may provide different criteria for
surface determination, but in the present exercise the coefficients aij were sought for
the nfhdegree surface,
U' = cn s
s=O r=O
as,uS-'u' .
The constant term aoomust remain undetermined, as for a surface defined entirely
by the slope of tangential planes the zero level must bc arbitrary.
Such a surface of degree n thus has n(n+3)/2 unknown coefficients to be calculated
and each station gives two separate equations,
for known u and u, the station coordinates of position. The number of stations
needed to determine an nrhdegree surface is thus the integral part of [n(n+ 3)/2+ 1]/2.0 I 2 3 4 5 6 CONTOUR UNITS
, 0.5 , \ \
SCALE FOR PARKINSON VECTORS
FIG.8. Parkinson vectors for period 80min, and the response surface fitted to
them. The contour values are heights of the surface relative to an arbitrary zero
level (and correspond to negative values of w as defined in the text).Array experiment with magnetic variorneters 61
Twenty-two stations are therefore sufficientfor an eighth degree surface, and 27 stations
would be needed for a ninth degree surface. To make full use of the data from the
present 26 stations, the values of A, and Br as given in Table 1 were fitted to
9 5
B, = C rasruS-' 6-'
s=l r=O
(7)
with u9,, and a95arbitrarily set to zero, because 26 stations are not sufficient for a full
ninth degree surface.
The coefficients ail were determined directly by solution of the 52 equations
obtained from writing (6) and (7) for each of the observing sites. These coefficients
were then used to generate a surface according to equation (5), and this is presented
in Fig. 8 as a contour map, relative to an arbitrary zero 1evel.The important problem
of smoothing the surface has not been attempted, and in the two northern corners of
the area there are steep undulations which have not been fully contoured.
The surface of Fig. 8 is just one of an infinite family which would fit the data,
and it is presented as an example of how Parkinson vectors for a number of sites can
be synthesized together. The advantage of such a map is that, unlike the maps of
Figs 5, 6 and 7, it summarizes the response in the vertical field for all polarizations of
variation in the horizontal field. If an optimum smoothed surface of this type were
to be determined, it could be used to predict the vertical variations occurring at any
point in the area, for any polarization of the horizontal fields.
The surface does not represent directly the level (or change in level) of any physical
quantity in the area covered. However, in conjunction with a similar surface for
A,, B,data, it contains in principle all information available from the analysis carried
out so far. One method of interpretation might therefore aim at inverting such
surfaces to give electrical conductivity distributions, especially if the surfaces have
been determined using data from stations that were not occupied simultaneously.
Indeed, an advantage of such surfaces is that their detail can be augmented by single
station operation at subsequent times. However, when magnetic variation data right
across such a large area has been recorded simultaneously, as in the present instance,
it is in principle possible to separate the variations into normal and anomalous patts,
(Porath, Oldenburg & Gough 1970). Further information, more valuable for inter-
pretation purposes, may come from such a separation exercise, and one will be
attempted in a subsequent paper.
The inter-relationships between the observed data, the polarization, the Parkinson
vector, and the in-phase response surface may be seen by comparing the Z amplitude
diagram of Fig. 5 with Fig. 8. The Parkinson vector points up the direction of steepest
slope of the response surface, and a short vector corresponds to a small slope. At
Echuca (ECH), for example, the component of the vector in the direction of the
horizontal polarization is small: thus the slope in the response surface at that azimuth
is low, and the 2 amplitude observed is low. At Mallacoota (MCT), by contrast, the
component of the Parkinson vector in the polarization direction is large, and the
corresponding 2 amplitude is high.
Discussion
The dominant feature of the results, in all the different forms of presentation, is
the correlation of strong Z variation fields with the coastlines. The different polariza-
tions of the horizontal fields in Figs 5,6 and 7 distinguish the response of the different62 F. E. M.LiUey and D. J. Bennett
coastlines one from the other. The Z response at the corner coastal station, Malla-
coota, is particularly strong (see Figs 2 and 3).
The phase maps are generally less distinctive than the amplitude maps, and phases
have been omitted for the almost linear polarizations of Fig. 7. However, the Z-phase
of Fig. 6 has a distinctive and strong pattern, which may bear explanation. It can
be seen that there is a total phase difference of 26 min across the map, corresponding
to a quarter of a period. The reason for this becomes clear if the X and Y fields are
considered resolved along the major and minor axes of the horizontal polarization
ellipse, to give fields of X' and Y', say, as shown in Fig. 9. The X' and Y' fields will
be an out of phase: the first, X', is almost perpendicular to the east coast, and the
other, Y', is almost perpendicular to the coast near the south-west corner of the array.
The Z phase map then rather clearly divides the Z amplitude response into a contribu-
tion from the east coast, in phase with the X' field, and a contribution from the south-
west coast, in phase with the Y' field. A similar exercise for Fig. 5 is less productive,
but the resolution of the horizontal fields into components parallel to the axes of
polarization can be seen to have valuable applications, and it will be the subject of
further investigation.
From the horizontal field maps of Figs 5 and 7 it is clear that for the east coast,
adjoining the Tasman Sea, the very strong coast-effect inZ is accompanied by virtually
no anomalous horizontal variations. The south-west coast, from the Bass Strait to
the Great Australian Bight, shows a more complicated response. In Fig. 6, for a
horizontal field polarized mainly perpendicular to it, the south-west coast shows the
usual strong Z variation with negligible horizontal anomalous field. However for the
other polarizations of Figs 5 and 7 a strong Z variation is still present, now with
considerable strength also in the X and Y fields. Particularly striking, in Fig. 7, is
the tendency for the Z contour lines to bow south into the Bass Strait while the X
contour lines bow northwards inland.
In an area so strongly dominated by the coast effect, other anomalous responses,
(of possible continental origin), may not be apparent so readily. However there is
evidence of departure from the usual coast effect in the observations at the stations
Hamilton (HTN),Derrinallum (DNM), and Ararat (ART), in the south-west corner
of the array. Stronger horizontal variations are observed, and slightly stronger
vertical variations, (see Fig. 5). The Parkinson vectors are deflected eastwards from
the usual pattern, (see Fig. 8). It is possible that the effects are connected with the
FJG.9. Resolution of horizontal field components, X and Y,along directions
parallel with the major and minor axes of the horizontal polarization ellipse.Array experiment with magnetic variometers 63
higher heat flows of the Victoria ' Newer Volcanics ', (marked on Fig. 1(6)). However
it will be necessary to interpret this anomaly in conjunction with the change in the
coastline from one of deep ocean (the Great Australian Bight) to one of shallow seas
(the Bass Strait) which occurs nearby.
Pending quantitative model fitting, a tentative interpretation of the main features
of the maps may be summarized as follows. Strong coast effects are observed in the
vertical fields near the edges of deep oceans, but not near the edge of a shallow sea
(the Bass Strait). The strong vertical variations occur for horizontal fields polarized
normally to a coast line, but they are not accompanied by anomalous horizontal
variations. Near the south-west coast of Victoria there is a continental anomaly,
which responds strongly in the vertical component when the horizontal fields are
.polarizedapproximately southeast-northwest. Anomalous variations in the horizontal
fields also occur in this region. It is unlikely that such large horizontal field anomalies
could be caused solely by a near surface effect, such as current channelling in the
Bass Strait. Therefore both vertical and horizoctal anomalous components could be
connected with the high heat flow region of the nearby recent volcanics.
Acknowledgments
The exercise was made possible by the generosity of Professor D. I. Gough, who
kindly lent his array of instruments to the authors, during the second half of his
sabbatical visit to the Australian National University. He is thanked for his advice
and assistance at all stages of the work.
Mr. P. M. McGregor assisted in locating the records for Toolangi. Many people
gave valuable help during the field operations, especially the pilot, Mr. M. Thorpe.
One of the authors, (D.J.B.), is the recipient of a research scholarship awarded
by the Australian National University.
Department of Geophysics and Geochemistry
Australian National University
Canberra
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